نقش استراتژی تعمیر در به حداقل رساندن هزینه گارانتی: تحقیق از طریق فرآیندهای شبه نوسازی

Most companies seek efficient rectification strategies to keep their warranty related costs under control. This study develops and investigates different repair strategies for one- and two-dimensional warranties with the objective of minimizing manufacturer’s expected warranty cost. Static, improved and dynamic repair strategies are proposed and analyzed under different warranty structures. Numerical experimentation with representative cost functions indicates that performance of the policies depend on various factors such as product reliability, structure of the cost function and type of the warranty contract

Extensive warranties are commonly offered by a wide range of manufacturers as a means of survival in increasingly fierce market conditions. Faced with the challenge of keeping the associated costs under control, most companies seek efficient rectification strategies. In this study, different repair strategies are developed and investigated under one- and two-dimensional warranties with the intent of minimizing the manufacturer’s expected warranty cost. Quasi-renewal processes are used to model the product failures along with the associated repair actions. Based on quasi-renewal processes, three different repair policies – static, improved and dynamic – are proposed, and representative cost functions are developed to evaluate the effectiveness of these alternative policies. In a one-dimensional warranty, the warrantor agrees to rectify or compensate the customer for the failed items within a certain time limit after time of sale. A two-dimensional warranty is a natural extension where the warranty period is characterized by a region defined simultaneously by time and usage. Examples of two-dimensional warranties are widely seen in the automotive industry where vehicles are covered under warranty until a certain age or mileage after the initial purchase. Karim and Suzuki (2005) provide a recent survey of the literature on statistical models and methods for warranty analysis. They present a summary of important mathematical findings such as estimators of critical parameters used in the analysis of warranty claim data. Thomas and Rao, 1999 and Murthy and Djamaludin, 2002 are also important review papers on product warranty. Thomas and Rao (1999) adopt a management perspective and focus on the works that address quantification of warranty costs and determination of warranty policies. They also present some research directions. Murthy and Djamaludin (2002) follow a broader perspective. They build on Murthy and Blischke, 1992a and Murthy and Blischke, 1992b paper and cover the pertinent academic developments in the areas of cost analysis, engineering design, marketing, logistics and management systems. They also mention applications in some other related areas such as law, accounting, economics and sociology. Of particular interest for the current study is the modeling of rectification actions in the warranty context. Majority of the literature on one- and two-dimensional warranties considers perfect and minimal repairs. Imperfect repair is widely modeled as a combination of perfect and minimal repair. Barlow and Hunter (1960) are the first to combine the perfect and minimal repair under one-dimensional warranties. The studies of Cleroux et al., 1979, Boland and Proschan, 1982, Phelps, 1983 and Nguyen and Murthy, 1984 give some other examples of combination repair/replace models under one-dimensional warranty. Choi and Yun (2006) investigate the performance of several functions to calculate a threshold limit on the acceptable cost of minimum repair. Their model replaces the failed product if the expected cost of minimum repair exceeds the predetermined threshold. Iskandar and Murthy, 2003, Iskandar et al., 2005, Chukova and Johnston, 2006 and Chukova et al., 2006 apply the combination type imperfect repair models in the context of two-dimensional warranties. In these four papers, warranty region is divided in various ways into disjoint sub-regions with a priory decision on whether to pursue minimum or complete repair within each region. The objective is to determine the sub-regions so as to minimize the expected warranty cost. An alternative approach is a generalization of the renewal process in which the product failure characteristics are revised after each failure as in the virtual age model proposed in Kijima (1989). In this model, the virtual age of the failed product is adjusted by a factor that reflects the degree of repair so as to bring it to a desired state somewhere between as good as new and as bad as old. Yanez et al. (2002) propose the use of Bayesian and maximum likelihood methods to estimate the model parameters for the generalized renewal process. Dagpunar, 1997 and Dimitrov et al., 2004 use modified versions of the virtual age model. Wang and Pham, 1996a, Wang and Pham, 1996b and Bai and Pham, 2005 use a further alternative and model the imperfect repairs in a single-dimensional warranty context as a quasi-renewal process. In the current paper, we extend their methodology to multi-dimensional warranties and adopt the appropriate version in both one and two-dimensional analyses. Due to the significance of the chronological age in warranty applications, quasi-renewal processes have greater intuitive appeal than the virtual age models in a warranty context. Quasi-renewal processes yield a mathematically convenient approach to calculate the number of failures within the warranty period. The remainder of the paper is organized as follows. Section 2 presents a detailed description of the problem. Section 3 describes the methodology used to model the failure and repair process, defines a representative cost function, and develops different repair strategies. Renewal equations are also characterized in this section to calculate the expected number of failures under different types of two-dimensional warranties. Section 4 presents an application of the proposed approach in a real life industrial example. The approach is investigated under a variety of settings through computational experimentation in Section 5. Section 6 concludes the paper and offers some suggested directions for future research.

Computational results show that the dynamic policy generally outperforms both static and improved policies on highly reliable products, whereas the improved policy is the best performer for products with low reliability. Although, the increasing number of factors arising in the analysis of two-dimensional policies renders generalizations difficult, several insights are offered for the selection of the rectification action based on empirical evidence. As a future direction, the analysis can be extended to multi-dimensional warranties. For example, a three-dimensional quasi-renewal process may be used to model the warranty policy offered for the flight engines. In addition, the study can be generalized to accommodate multi-component systems. In this case, each component failure process may be modeled as a quasi-renewal process.